Cremona's table of elliptic curves

610 = 2 · 5 · 61

Field	Data	Notes
Atkin-Lehner	2- 5- 61-	Signs for the Atkin-Lehner involutions
Class	610c	Isogeny class
Conductor	610	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	4880 = 24 · 5 · 61	Discriminant
Eigenvalues	2-  2 5-  0 -6  6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5,-5]	[a1,a2,a3,a4,a6]
j	13997521/4880	j-invariant
L	3.2804783161188	L(r)(E,1)/r!
Ω	3.2804783161188	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4880h1 19520d1 5490f1 3050a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 610c1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	2	-	0	-6	6	6	-4	4	-2	-10	2	-2	-12	-2	6	14	-	8	-10	-14	6	6	-6	10

---

Quadratic twists for elliptic curve 610c1

-4	8	-3	5	-7	-11	13	61
4880h1	19520d1	5490f1	3050a1	29890r1	73810f1	103090c1	37210b1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations